Chapter 6 - Inference for Categorical Data / Exercise 6.5

In a 2010 Survey USA poll, 70% of the 119 respondents between the ages of 18 and 34 said they would vote in the 2010 general election for Prop 19, which would change California law to legalize marijuana and allow it to be regulated and taxed. At a 95% confidence level, this sample has an 8% margin of error. Based on this information, determine if the following statements are true or false, and explain your reasoning.

Answer

  1. We are 95% confident that between 62% and 78% of the California voters in this sample support Prop 19.

False: Due to the fact that confidence interval is constructed to estimate the population proportion, not the sample proportion as it is stated.

  1. We are 95% confident that between 62% and 78% of all California voters between the ages of 18 and 34 support Prop 19.

True: Due to the fact that confidence interval is constructed to estimate the population proportion and from the above statement we have as follows:

95% CI: 70%±8%; which means 95% CI goes from 70%???8%=62% to 70%+8%=78%.

  1. If we considered many random samples of 119 California voters between the ages of 18 and 34, and we calculated 95% confidence intervals for each, 95% of them will include the true population proportion of 18???34 year old Californians who support Prop 19.

True: By the definition of the confidence level.

That is: Constructing a confidence interval for a proportion:

Verify the observations are independent and also verify the success-failure condition using p^ and n.

If the conditions are met, the sampling distribution of p^ may be well approximated by the normal model.

Construct the standard error using p^ in place of p and apply the general confidence interval formula.

  1. In order to decrease the margin of error to 4%, we would need to quadruple (multiply by 4) the sample size.

True: Quadrupling the sample size decreases the SE and ME by a factor of 14???=12.

  1. Based on this confidence interval, there is sufficient evidence to conclude that a majority of California voters between the ages of 18 and 34 support Prop 19.

True: The 95% CI is entirely above 50%.